The hydraulic resistances of the intima and media determine water flux and the advection of macromolecules into and across the arterial wall. Despite several experimental and computational studies, however, these trans- port processes and their dependence on transmural pressure remain incompletely understood. Here we use a combination of experimental and computational methods to ascertain how the hydraulic permeability of the rat abdominal aorta depends on these two layers and how it is affected by structural rearrangement of the media under pressure. Ex vivo experiments determined the conductance of the whole wall, the thickness of the media, and the geometry of medial smooth muscle cells and extracellular matrix. Numerical methods were used to compute water flux through the media. Intimal values were obtained by subtraction. A mechanism was iden- tified that modulates pressure-induced changes in medial transport properties: compaction of the extracellular matrix leading to spatial reorganisation of smooth muscle cells. This is summarised in an empirical constitutive law for permeability and volumetric strain. This led to the physiologically interesting observation that, as a consequence of the changes in medial microstructure, the relative contributions of the intima and media to the hydraulic resistance of the wall depend on the applied pressure; medial resistance dominated at pressures above ∼93mmHg in this vessel.